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3 years ago

The sum of three consecutive integers is 18. Write an equation for this situation and then find the three integers.

Mathematics

2 answers:

Aleonysh [2.5K]3 years ago

6 0

3x=18 is the equation

the 3 integers are 6 because 6*3=18

Sedaia [141]3 years ago

4 0

X+y+z=18
and the three integers are 5,6, and 7

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A rectangle has a length of 34 inches less than 5 times it’s width. If the area of the rectangle is 867 square inches, find the

pshichka [43]

Length of the rectangle is 51 inches

Solution:

Given that

Length of the rectangle in 34 miles less than 5 times its width

Area of rectangle = 867 square inches

Need to determine length of the rectangle.

Let assume width of the rectangle be represented by variable x.

So 5 times width of the rectangle =5x

34 inches less than 5 times width of the rectangle = 5x – 34

As Length of the rectangle in 34 miles less than 5 times its width

=> Length of the rectangle = 5x – 34

The formula for rectangle is given as:

$\text { area of rectangle }=length \times width$

As given that Area of rectangle = 867 square inches

$\begin{array}{l}{=>867=(5 x-34) \times(x)} \\\\ {=>5 x^{2}-34 x-867=0}\end{array}$

On solving quadratic equation by using quadratic formula

$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

In our case a = 5, b = -34 and c = -867

On substituting value of a, b and c in quadratic formula we get

$\begin{array}{l}{x=\frac{-(-34) \pm \sqrt{(-34)^{2}-4 \times 5 \times(-867)}}{2 \times 5}} \\\\ {=>x=\frac{34 \pm \sqrt{18496}}{10}=\frac{34+136}{10}} \\\\ {=>x=\frac{34+136}{10}=17 \text { or } x=\frac{34-136}{10}=-10.2}\end{array}$

Since x represents width, it cannot be negative, so x = 17

Length of the rectangle = 5x – 34 = 5(17) – 34 = 51

Hence length of the rectangle is 51 inches

5 0

3 years ago

What is the equation in point−slope form of the line passing through (2, 2) and (4, 8)?

irina [24]

It is definitely (y-2)=3(x-2)

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3 years ago

Write an equation of the parabola that opens up whose vertex (−1, 2) is 3 units from the focus. (Vertex form or Parabola Form is

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Answer:

y2 = 4ax (opens right, a > 0)

y2 = -4ax (opens right, a > 0)

x2 = 4ay (opens up, a > 0)

x2 = -4ay (opens down, a > 0)

Vertex at (h, k) :

(y - k)2 = 4a(x - h) (opens right, a > 0)

(y - k)2 = -4a(x - h) (opens right, a > 0)

(x - h)2 = 4a(y - k) (opens up, a > 0)

(x - h)2 = -4a(y - k) (opens down, a > 0)

Equation of a Parabola in Vertex form

Vertex at Origin :

y = ax2 (opens up, a > 0)

y = -ax2 (opens down, a > 0)

x = ay2 (opens right, a > 0)

x = -ay2 (opens left, a > 0)

Vertex at (h, k) :

y = a(x - h)2 + k (opens up, a > 0)

y = -a(x - h)2 + k (opens down, a > 0)

x = a(y - k)2 + h (opens right, a > 0)

y = -a(y - k)2 + h (opens left, a > 0)

Step-by-step explanation:

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Ilia_Sergeevich [38]

Answer:

your answer would be D....

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3 years ago

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olya-2409 [2.1K]

Answer:

make the denominators ( bottom number ) the same and whatever u do to that do to the top

Step-by-step explanation:

e.g ½ - ⅓

make the common denominator 6

to get from 2 to 6 u times by 3 so it wud be 3/6

and then to get from 3 to 6 u times by 2 so do the same to the numerator (top number) so u get 2/6

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7 0

3 years ago

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